You're Correct!

The posture and a players spine angle can have a huge effect on the swing plane, overall power and consistency of shots.

If a golfers spine angle becomes too upright then the swing plane will most likely become too flat. If the spine angle becomes too tilted then the swing plane can become too upright.
The swing plane is the inclined path the club takes when swung around the body. If a plane is flat it will resemble more of a baseball swing (around the body). If its too upright it will resemble an amusement park pirate ship (back and through, straight up straight down). Most golfers will want a plane which moves around the body on a mostly horizontal axis in relation to the spine angle. Its the tilt of the spine which allows the swing plane to also become tilted on its side. The first thing golfers need to accomplish is an effective and strong golf posture for their body size and shape. Use this drill to establish a good posture.

Hold the club in front of your belly button with your legs straight. Stand up tall with your shoulders pulled back and stick your chest out. The arms should be extended with the biceps pressing in slightly to either side of the chest.
Tilt forwards making sure the hips stay back and the lower back remains flat rather than rounded. Feel like you are pushing your pelvis back.
As the club lowers to touch the ground behind the ball, flex your knees slightly. The feeling should be just a bounce in the knees and not an exaggerated bend.

The result of this drill should be a tilted spine angle and appropriate for your height and club length.

Taller golfers will tend to find they have a more upright plane as they are usually more tilted over the ball whilst short golfers will tend to have a flatter plane as their spine angle is usually more upright in relation to the ground.

Although the spine angle will greatly affect the swing plane, the hip rotation will have a bigger impact on the overall power generated throughout the swing and should not overly affect the plane. Also, the hips can rotate with an upright or flat spine angle.

People often think that moving the head during the swing will alter the spine angle. Remember the head has no muscles that can move the body, its the body which can move the head. Focus on keeping the hips back, the spine straight and the knees flexed.

The swing plane can be made to look good by manipulating how the hands lift the club. However, for a consistent and powerful swing plane the spine needs to be tilted correctly with a strong posture underpinning it. Using a correct posture will enable a strong spine angle and a consistent swing plane.